What does it mean you've undated "directx firmware"? Firmware is software stored on flash memory located on graphics card itself, drive is something you install to your harddrive and which is used by your operating system to know how to communicate with the graphics card, and DirectX is some kind of abstraction layer common between GPUs (GPUs are made compatible with DirectX, not the other way around, thus differing from drivers). They're three different things. And all of them are updatable.
My suggestions:
- which ever of the three you updated, update the lacking two
- run Prime95 in Torture Test mode to check for stability. It'll run fast Fourier transformations (FFT) and compare the results of known correct answer, trying to find system instability caused by miscalculation.
- try different screen resolutions.
If the lines are present always, even during BIOS POST or BIOS setup screen, exclude driver and DirectX from possible cause. Also excuse northbridge overheating from explanation as it takes several minutes to heat up to the point of showing any instability. GPU hardware or GPU firmware is the problem. Alternatively it could be that motherboard is permanently damaged and doesn't even function normally even when it's not overheated. (If the problems are limited to graphics, then is likely GPU and not motherboard that is toast.)
If the lines aren't there during boot but are present immediately after the boot it may be related to anything software, firmware or hardware. It can be explained by lines being present only with certain resolutions (boot-up procedure doesn't typically use a high resolution). The lines appearing immediately after boot should also excuse overheating of northbridge or overheating of GPU as possible cause. Even if fan failed they'd stay relatively cool for some minutes.
If problems aren't immediately present when booted to Windows but appear soon after, your hardware is toast and/or overheating. No driver, directX or firmware update can save it, fan swap can possibly fix it (unless the fan on GPU is already working, in which case replacing it wouldn't probably do anything (as long as it spins even a little is usually enough to provide bare minimum amount of cooling to keep it stable (especially under 2D use (no 3D acceleration)).
Yeah, I've had GPU issue with... with 2 or 3 cards so far. First was some old ATI card that seized it's fan. I replaced it with a passive heatsink (a small northbridge heatsink torn from a dead motherboard), making it stable for up to 30 minutes of high GPU load. Not good for gaming fix but even years later, it's still used for web surfing and perfectly stable at that. No "artefacts".
Also slightly problematic were passively cooled ATI HD2400Pro and nVidia 6200 (both passively cooled from factory). Both had their share of oddities. Too bad I don't remember what exactly they issues were.
Nowadays running passively cooled (this time with heatpipes) Sapphire ATI HD4670. This is actually problem free GPU *touch wood*. And a killer performer for a passive one. In fact the Sapphire's cooling solution is more effective than the fan-based variants using the same ATI chip. Never managed to get it overheated, not even during FurMarking (like Prime95 torture test but tortures GPU instead of CPU).
If the lines appear only after it has warmed up, and you've made sure it's not GPU at fault, swapping northbridge cooler may help. There are however other components on motherboard that heat up. It's not usually northbridge overheat that causes issues but capacitor leakage/drying (accelerated by long-term overheating). Capacitor trouble may become worse when warmed up but can also be present on cold starts. Potential trouble include:
instability during Prime95 (though it mainly tests CPU for calculation errors)
odd system freezes that don't necessarily even give you bluescreen of death
incapability to boot or inconsistent boot-up success (immediate freezes to freezes in midway to booting OS)
data corruption on stuff that is written to HDDs
I've had to fix two of my computers that suffered from capacitor plague. Desolder electrolytic caps (usually Chinese crap) and replace them with low-ESR Japanese-made capacitors rated for 105 deg C (standard 85 deg C isn't good for elcaps located near hot components).
Here's something to read to make a visual inspection:
http://en.wikipedia.org/wiki/Capacitor_plagueNote that out of the two I fixed, only one showed visible signs of capacitor plague.